I have little to no sex drive (am "asexual" as the kids say), but I've had intense crushes/obsessive feelings about individuals with no associated desire to have sex with the targets thereof.
I imagine that for people with normal sex drives, both components play a role in initial relationship formation; ie, there's an emotional component in addition to "lust" as conventionally defined.
You could quibble that these (relatively short lived) intense emotions are "lust", as opposed to the "love" of a longer relationship, but that seems to be playing a semantic game that doesn't really concord with how we generally use those words.